International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by Th. Hahn

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. A. ch. 1.1, p. 3

Section 1.1.6. Motions and matrices

Th. Hahna*

a Institut für Kristallographie, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany
Correspondence e-mail: hahn@xtal.rwth-aachen.de

1.1.6. Motions and matrices

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Printed symbol Explanation
W ; M Symmetry operation; motion
(W, w) Symmetry operation W, described by an (n×n) matrix W and an (n×1) column w
W Symmetry operation W, described by an (n+1)×(n+1) `augmented' matrix
I ( n × n ) unit matrix
T Translation
(I, t) Translation T, described by the (n×n) unit matrix I and an (n×1) column t
T Translation T, described by an (n+1)×(n+1) `augmented' matrix
I Identity operation
(I, o) Identity operation I, described by the (n×n) unit matrix I and the (n×1) column o
I Identity operation I, described by the (n+1)×(n+1) `augmented' unit matrix
r , or x Position vector (of a point or an atom), described by an (n+1)×1 `augmented' column
(P, p); or (S, s) Transformation of the coordinate system, described by an (n×n) matrix P or S and an (n×1) column p or s
P ; or S Transformation of the coordinate system, described by an (n+1)×(n+1) `augmented' matrix
(Q, q) Inverse transformation of (P, p)
Q Inverse transformation of P








































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